Drop rate
Drop Rate is the frequency at which a monster is expected to yield a certain item when killed by players. When calculating a drop rate, divide the number of times you have gotten the certain item, by the total number of that NPC that you have killed. For example: *Bones have a 100% drop rate from chickens. *Feathers have approximately a 75% drop rate from chickens. Drop rate All items have a chance of being dropped that is expressible as a number, their drop rate. Drop rates are not necessarily a guarantee; an item with a drop rate of "1 in 5" does not equate to "This item will be dropped after 5 kills." While each kill does nothing to increase the drop rate itself, it is trivial to state that more kills gives rise to more chance overall. A popular misconception is that you are guaranteed that item when you kill the NPC n'' number of times, where \frac{1}{n} is the drop rate. You are '''never' guaranteed anything, no matter how many of that monster you kill. For example: If the King Black Dragon is expected to drop a Draconic visage once out of 5,000 kills, then the probability that you will get at least one drop in 5,000 kills is: : \begin{align} & 1-\left(1-\frac{1}{5000}\right)^{1} \\ = & \ 1-\left(\frac{4999}{5000}\right)^{1}\\ = & \ 1 - 0.9998 \\ = & \ 0.0002 \\ \end{align} Which is approximately 0.02%. Similarly, we can solve for the number of KBDs you need to kill to have a 90% probability of getting one when you kill them: : \begin{align} & \ 1-\left(\frac{4999}{5000}\right)^{x} \approx 0.90 \\ & x = \frac{ln(1-0.9)}{ln(\frac{4999}{5000})} \\ & x \approx 11511.774 \approx 11512 \\ \end{align} Which yields the answer 11,512. Thus, we have shown that, while being counterintuitive, drop rates are not what they seem to be. Binomial model Given a known value of \frac{1}{x} , the chance of receiving such an item k times in n kills can be calculated using . The probability of receiving an item k times in n kills with a drop rate of \frac{1}{x} = p follows: : \binom n k p^k(1-p)^{n-k} where \binom n k =\frac{n!}{k!(n-k)!} For finding the probability of a obtaining an item at least once, rather than a specified number of times, we can drop the binomial coefficient and simply the equation to: : 1 - (1 - p)^x Where (1-p)^x is calculating the probability of not receiving the item, and we use that to calculate the inverse. For example, it is known that the drop rate of the Draconic visage is \frac{1}{10000} = 0.0001 . If we want to know the probability of receiving one visage in a task of 234 Skeletal Wyverns, we would plug into the equation: : \begin{align} & 1 - (1 - 0.0001)^{234} \\ = & \ 1 - 0.9999^{234} \\ \approx & \ 1 - 0.97687 \\ \approx & \ 0.023129 \end{align} Giving us the answer, we have approximately a 2.3% chance of receiving a visage during this task. Elusive drops Below is a table of the rarest and most sought-after drops in Old School RuneScape. Also, the kill count or number of kills required is based on a 90% probability of getting the drop. See also *Drops *Rare drop table *Items *Bestiary Category:Needs drop table Category:Mechanics